The Scottish side were dumped out of the Europa League by Kuban Krasnodar in Russia on Thursday.
"I don't want to make any excuse but I know what it was like last season against St Mirren (following a Europa League game at Levante) when we were hanging on with 20 minutes to go," PA Sport quotes McCall as saying. "I thought, to get anything out the game, we needed to be going into the last 20 minutes ahead.
"It's only natural, you get back in your bed at seven o'clock in the morning after the flight. If you're still in there you can dog it out, but when you lose two goals like that, you could see the lift they got and we looked a bit leg-weary.
"The better team won. You can't afford to gift teams goals, especially good teams like Aberdeen who have threats all over the park."
Motherwell take on Inverness Caledonian Thistle in their next encounter.